Solve for $x$ and $y$ using elimination. ${-4x-2y = -36}$ ${3x+2y = 28}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $-x = -8$ $\dfrac{-x}{{-1}} = \dfrac{-8}{{-1}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {-4x-2y = -36}\thinspace$ to find $y$ ${-4}{(8)}{ - 2y = -36}$ $-32-2y = -36$ $-32{+32} - 2y = -36{+32}$ $-2y = -4$ $\dfrac{-2y}{{-2}} = \dfrac{-4}{{-2}}$ ${y = 2}$ You can also plug ${x = 8}$ into $\thinspace {3x+2y = 28}\thinspace$ and get the same answer for $y$ : ${3}{(8)}{ + 2y = 28}$ ${y = 2}$